In this paper, we classified a class of fourth-order partial differential equations (PDEs) to be fourth-order PDE of type I, II, III and IV. The PDE of type IV is solved by using an efficient numerical method. The PDE is first transformed to a system of fourth-order ordinary differential equations (ODEs) using the method of lines, then the resulting system of fourth-order ODEs is solved using d...

Abstract A spectral‐Galerkin method based on Legendre‐Fourier approximation for fourth‐order problems in cylindrical regions is studied this paper. By the coordinate transformation, a three‐dimensional problem region transformed into sequence of decoupled with two dimensions and corresponding pole conditions are also derived. With appropriately constructed weighted Sobolev space, weak form esta...